Question

Which of the following shows the prime factorization of 200 using exponential notation?

Answer 1

Answer:

The prime factorization of 200 using exponential notation is $2^{3}\times 5^{2}$.

Step-by-step explanation:

First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.

1) $\frac{200}{2} = 100$ (Even number)

2) $\frac{100}{2} = 50$ (Even number)

3) $\frac{50}{2} = 25$ (Even number)

4) $\frac{25}{5} = 5$ (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

5) $\frac{5}{5} = 1$ (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

Now, we construct the prime factorization using exponential notation:

$200 = 2^{3}\times 5^{2}$

The prime factorization of 200 using exponential notation is $2^{3}\times 5^{2}$.